Freakonomics had an episode with an economist that worked with Ebay on ad buys. This sort of "buy ads on your own keywords" was shown to have zero impact on sales to the point that they cut completely stopped advertising when the search included "ebay".
This will work for someone like eBay (people searching eBay want eBay) but for other "brand-name" terms it may NOT work - people searching for Travelocity or whoever is the hotness there may be perfectly happy with the first "similar enough" link.
There's no way to know until they do an A/B test like eBay did I guess. EBay was certain that they needed to do the on brand ads before this economist showed up too.
It's when the phrase is at or near generalization that it comes into play - someone searching for Kleenex likely doesn't care what tissue they find, and many people who Google Google would be happy to click Bing if it popped up first.
"Dominos" might be one where people wouldn't mind ordering from Pizza Hut as they're using it as a generic term for pizza.
eBay is a strong brand where people searching for eBay are going to click on eBay, almost no matter what. For other less recognizable brands or crowded categories, this is often not the case.
Branded search terms are almost always less incremental than non-branded (ie: "lodge logic" vs. "cast iron skillet"), but the actual incrementality of the terms is something every advertiser should be testing continuously.
